SERIAL CORRELATION

In Panel data

Chapter 5(Econometrics Analysis of Panel data -Baltagi)

Shima Goudarzi

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As We assumed the stndard model:

and

(No Matter how far t is from s)

The regression disturbances are homoscedastic with the

same variance across time and individuals.

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� This assumption cannot be always true

For example in Investment, Consumption a shock affects

the behavioral relationship for at least the next few periods.

� Using the routine solution results in:

consistent but inefficient estimates of regression coefficients

and biased standard errors.

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Serial Auto regression AR(1) in νit

(Willis- Lillard 1978)

� They generalized the error component model to the

serially correlated case, by assuming that

lρl<1

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Baltagi and Li (1991) applied the Prais-Winstten transformation

matrix ,to transform disturbances into serially uncorrelated

classical errors.

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First step :They suggest estimating � from Within

esiduals �� it as :

-for large T

-for small T

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Second step: Estimating , by substituting OLS residuals ��

in this equation:

Then, Estimating and From

Where

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Empirical Application AR(1)

Lillardand Weiss(1979) used the panel earnings data on

American scientists over the decade 1960-70 to analyze the

covariance structure of earnings over time .

Ln Yit = Xit β+ Uit

Yit : real annual earnings of the ith person in the tth year

x : dependent variables like ,experience ,gender,

employment in private industry .

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μi Represents unmeasured characteristics such as ability and work on the

relative earning of scientists (individual effects).

Represents the effect of omitted variables which affect the growth of

earning like learning ability.

Transitory but serially correlated differences, represents the rate of

deterioration of the effect of random shock εit on which persists over a

year.

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They used the Maximum likelihood to estimate the

parameters of the residual and then applied GLS to

estimates β.

By comparing the actual and predicted covariances, we see that

their specification is quite successful in predicting the pattern.

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Serial Auto regression AR(2) in νit

The transformation can allow also for AR(2) process on the νit

where

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The matrix C defined

The first step is transforming the data by the C Matrix

And then obtain GLS on model by computing .

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Unequally Spaced Panels with AR(1) Disturbances

(Baltagi 1991)

Sometimes panels cannot be collected every period due to

lack of resources or cut in data.

� Panel daily data from stock market that is unequally

spaced when the market closes on holidays.

� Housing resale data when the pattern of resale for each

house occurs at different time periods.

In this paper Baltagi and Wu tried to estimate an unequally

spaced panel data regression model with Random effect and

AR(1)disturbances.

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Random

Effect(GLS)

Random Effect GLS with

AR(1)

β1 0.11(0.011) 0.095(0.008)

β2 0.308(0.017) 0.32(0.026)

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Random Effect and AR(1) and locally best invariant test(LBI

- The Baltagi –Wu LBI statistics: 0.95

- Durbin-Watson for : 0.68

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Jointly test of Serial Correlation and Individual Effects

Remainder disturbances AR(1) process

or MA(1) process

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Extensions

Other extensions include

� The fixed effect model with MA(q)Remainder

disturbances and also the treatment of Autoregressive

moving average ARMA(p,q) case on the νit.

� Extension to the two-way model with serially correlated

disturbances

� Chamberlain (1982, 1984) allows for arbitrary serial

correlation and heteroskedastic patterns by viewing each

time period as an equation and treating the panel as a

multivariate.

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Refrences:

-Becketti, S.,W. Gould, L. Lillard and F.Welch, 1988, The panel study of income dynamics after fourteen years: An evaluation, Journal of Labor Economics 6, 472–492

-Berry, S., P. Gottschalk and D. Wissoker, 1988, An error components model of the impact of plant closing on earnings, Review of Economics and Statistics 70, 701–707

Baltagi, B.H. and Q. Li, 1995, Testing AR(1) against MA(1) disturbances in an error component model,

Journal of Econometrics 68, 133–151.

-Econometric Analysis of Panel Data, 4th Edition ,Badi H.Baltagi,2008,Wiley

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